In order to estimate \(N_{\mathbf {a}}(B)\) , we apply a version of the circle method introduced by Duke, Friedlander and Iwaniec in [1]}, and refined by Heath-Brown in [2]}. The more classical forms of the circle method used in [3]} and [4]} are not sufficient for our purposes, but the version in [2]} is particularly well-suited to dealing with quadratic forms. In fact, in [2]}, Heath-Brown proves a vast generalisation of (REF ) by finding an asymptotic formula for the quantity
\(N_w(Q,B) = \sum _{\begin{array}{c}\mathbf {x}\in \mathbb {Z}^n\\Q(\mathbf {x})=0\end{array}}w(B^{-1}\mathbf {x}),\) 
